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Deep neural networks often require copious amount of labeled-data to train their scads of parameters. Training larger and deeper networks is hard without appropriate regularization, particularly while using a small dataset. Laterally,…
We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations,…
Random Matrix Theory (RMT) is applied to analyze weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5…
Regularization plays a vital role in the context of deep learning by preventing deep neural networks from the danger of overfitting. This paper proposes a novel deep learning regularization method named as DL-Reg, which carefully reduces…
The purpose of this article is to develop a machinery to study the capacity of deep neural networks (DNNs) to approximate high-dimensional functions. In particular, we show that DNNs have the expressive power to overcome the curse of…
In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…
Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent…
Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their…
Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…
Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…
Deep neural networks have had an enormous impact on image analysis. State-of-the-art training methods, based on weight decay and DropOut, result in impressive performance when a very large training set is available. However, they tend to…
Deep neural networks (DNNs) have become a crucial instrument in the software development toolkit, due to their ability to efficiently solve complex problems. Nevertheless, DNNs are highly opaque, and can behave in an unexpected manner when…
We investigate deep morphological neural networks (DMNNs). We demonstrate that despite their inherent non-linearity, "linear" activations are essential for DMNNs. To preserve their inherent sparsity, we propose architectures that constraint…
Convolution Neural Networks, known as ConvNets exceptionally perform well in many complex machine learning tasks. The architecture of ConvNets demands the huge and rich amount of data and involves with a vast number of parameters that leads…
Deep neural networks (DNN) have achieved remarkable success in various fields, including computer vision and natural language processing. However, training an effective DNN model still poses challenges. This paper aims to propose a method…
Normalization techniques are essential for accelerating the training and improving the generalization of deep neural networks (DNNs), and have successfully been used in various applications. This paper reviews and comments on the past,…
Deep neural networks (DNNs) frequently present behaviorally irregular patterns, significantly limiting their practical potentials and theoretical validity in travel behavior modeling. This study proposes strong and weak behavioral…
Deep neural networks (DNNs) have been deployed in myriad machine learning applications. However, advances in their accuracy are often achieved with increasingly complex and deep network architectures. These large, deep models are often…
Training neural networks is an optimization problem, and finding a decent set of parameters through gradient descent can be a difficult task. A host of techniques has been developed to aid this process before and during the training phase.…
Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…